For a nice discussion from the statistical point of view of the logarithmic transformation and how to interpret it, check out these topics on Cross Validated:

• In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?

• Interpretation of log transformed predictor.

• When (and why) to take the log of a distribution (of numbers)?

For some additional discussion about the case where you have zeroes:

• How should I transform non-negative data including zeros?

• How small a quantity should be added to x to avoid taking the log of zero?

For some more information about the use of the Box-Cox transformation and the aftermath, check out these topics on Cross Validated:

• Expressing answers in terms of original units in Box-Cox transformed data.

• Life after the Box-Cox transformation.

And, for some general discussion about transformations, see:

• What other normalizing transformations are commonly used beyond the common ones like square root, log, etc.?

The online Engineering Statistics Handbook discusses some of the operational details of finding data transformations in Section 4.6.3.3 Transformations to Improve Fit.